Without a minute understanding of what's involved, I'd guess that normalizing is a non-local operation, in the sense that the effect of normalizing some x depen

Without a minute understanding of what's involved, I'd guess that normalizing is a non-local operation, in the sense that the effect of normalizing some x depends on the other elements of your dataset, so that normalization includes the "information" of the rest of the data implicitly. In real life, that's sort of like having access to the answers when you're given the questions. Being trained in that environment won't do much good.